Calculating Player Values II - 3 comments

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This is the second part of an article describing in very general terms, how to calculate player values. If you’ve not read Part I, that would be a good first step as I’ll be assuming you have from here forward. You can find Part I here.

Back? Great. So in summary, Part I describes one method to derive quantitative values for projected stats in all standard roto categories. I want to talk briefly about some variations of this, and ways that you can apply these same concepts to different kinds of leagues. After that we’ll move on to talk about adjusting where needed for your roster requirements, and ultimately computing dollar values for you auction drafters.

So the first question you might have on your mind: is this the only way to compute player values? Well, no. But it is a pretty good one, though perhaps more complex than other methods you might encounter. And I would argue, better. There is one other method which I think has merit, and I think ultimately is at the heart of many formula-driven models. The basic principal is to look at some final league standings, and try to draw conclusions from that. I’m going to use the stats from one of my leagues last year as an example. In the runs category, the highest placing team compiled 1,098 runs. The team with the lowest total had 775 (ouch). This was a 12-team league, so there were 11 places separating the two. And they had a gap between them of 323 runs. So the team in 12th place could in theory move up one place in runs for every 29.36 runs they added to their total. In home runs, the spread was 291 to 189 (ouch again). Here, we see an average of 9.27 home runs needed to move up one position. So, 9.27 HR is about equal in value to 29.36 runs. And we would make the same calculation for every scoring category to arrive at a fairly basic formula we could use to estimate value.

So why not just do it this way? Well, this method has some challenges. Namely, do you have access to completed season stats for the league in which you are about to participate? I wouldn’t recommend using mine I just shared, as this was a 13-hitter/8-pitcher roster, probably not what you’re using. In many leagues you encounter dead or under-managed teams that don’t give a realistic idea of what the floor for each category should be. You would ideally want to compare final stats for as many leagues as you can that played in a format as similar to yours as possible, because there is so much variance that comes from manager ability, activity level, position eligibility, transaction limits, innings limits, bench size, etc. Undoubtedly you could likely look at final stats from two leagues with identical setups and find some wide variation in the spread of points amongst teams. That’s what I like so much about the standard deviation method. You are drawing your values based on how each player relates to every other player in your projections. And this makes it very easy to make adjustments should you need to add or change scoring categories. For instance I got invited to play in a league that uses OBP instead of runs. That’s right, taking a walk counts more than scoring a run, just like in real baseball! Well, no problem. I ran Z-scores on OBP the same way I did batting average, added this into my total instead of runs and in a matter of minutes I had player rankings for this new scoring system.

So how would you customize for different league configurations? Really, whatever stat you need to add should fall into one of two categories; it will either be a counting stat like home runs or a ratio stat like ERA. The counting stats are easy; just find the mean and standard deviation and run a Z-score. For any ratio stat you need to find a way to turn it into a “value-added” stat, like the way we previously discussed doing for batting average. What numbers go into the stat, and how much does each walk/run/K/GDP/etc. affect your team average? Then you run Z-scores on this new value you computed. This can be challenging for some creative scoring systems.

Position Scarcity

From here, we’re going to look more at GiantsFan14’s projections he has so generously shared with the Cafe community.

The final column here reflects the sum of all five Z-scores for the standard roto categories. And these are at this point completely independent of position, this is simply the score for each player’s projected stats regardless if he’s a first baseman, second baseman or catcher. How you adjust for position scarcity depends upon your league setup. For now, let’s assume the following:

12 team league
14 hitters (C,C,1B,2B,SS,3B,CI,MI,OF,OF,OF,OF,OF,UT)
9 pitchers
no bench

Honestly, even if I have a bench I don’t adjust my rankings or values at all. You could adjust slightly when you get to dollar values if you want. So what do we mean when we talk about scarcity anyway? Is the catcher position scarce? Every major league team has at least one, right, so shouldn’t there easily be 24 to go around? Well yes, but the problem is more that many of them are players you’d never pick to have on your team, but you have to due to the roster requirements. Let’s get a count real quick. Twelve teams, with each picking 14 hitters means we will be drafting 168 hitters. If we were to take a closer look at the top 168 hitters, we would see the following breakdown:

9 are eligible at C
32 are eligible at 1B
19 are eligible at 2B
18 are eligible at SS
20 are eligible at 3B
85 are eligible at OF

Look over those numbers again. We’re saying that if this were a league with no roster restrictions at all, just draft the best 14 hitters you can find, we would still draft 19 second basemen, 20 third basemen, nine catchers, etc. just because they were the best hitters available. Notice that these totals almost exactly align with the totals of each position we actually need to draft. Middle infield is exactly where it needs to be. For every team to draft a 2B, a SS, and a MI, we need a total 36 players in the 2B/SS totals and we have 37 that are in the top 168 on their own merits. Now, are there still tiers you should consider when evaluating which positions to fill? Certainly, but just don’t over-compensate. Every middle infielder taken will be rosterable. Now these are just the numbers we’re seeing in GF’s projections, but I will tell you I saw very similar totals in my own projections. And your league may vary. If you are only playing nine hitters, you likely will have to make some adjustments.

But for now, it looks like the only place we need to adjust is catcher. If we had our druthers, we would only take 9 of them, but we have to take 24. And this means if you happen to get one of those top few, you have a comparative advantage to a team that has to take the 24th catcher. And that’s where the term “value over replacement player” (VORP) comes from. The top catcher’s value is no longer simply what he contributes to your team, but it is now how much he contributes to your team versus the poor schmuck that waited until the end and is starting Nick Hundley. Lots of computations can be made here, but bottom line we need to artificially inflate the value of catchers until 24 of them fall into our draftable universe. There are several ways you could do this; I do something pretty simple. I look at the value of catcher No. 24, in this case Hundley. The current value of actual player 168, Casey Blake, is -0.958. Hundley is sitting at -3.355. We need to add a little more, because adding 15 catchers to the top 168 bumps Blake down by that many. If we were to add 3 points to every catcher, that should about do it.

Note that in making this adjustment to catchers, we also altered the positional content of our draftable universe for other positions. In this case, it’s still pretty close so I’m not adjusting it further. But you’ll just want to spot check yours again.

Dollar Values

As we have seen with computing player values and adjusting for positional scarcity, there is more than one method to determine dollar values for players. Again, I’ll show you one way and you can adjust as necessary for your situation. If you haven’t figured it out by now, my aim in this article is to equip you to do this for yourself, not to write a bunch of fluff then present you a finished product that’s exactly what you want. The aim is to teach you to fish, so to speak; not serve you up some parmesan crusted halibut with lemon caper sauce and a side of grilled asparagus.

And again, how we approach this next step depends upon the makeup of your league. We’ll keep the same roster configuration as before, which is a pretty common format. Let’s assume we have again a 12-team league, and we’re drafting via an auction, with a budget of $260. We’ll start with determining how much money we’re spending on hitting, and how much on pitching. I’m going to allow just as much for every pitcher as for every hitter, but not everyone does it this way. Some people use a 70/30 split, or 60/40, or anywhere in between. Our 23 man roster consists of 14 hitters and 9 pitchers. So 14/23, or 60.87%, of our roster is hitters. Each of the 12 teams has a $260 budget, so there are $3,120 in play. 60.87% of this would be $1,899, let’s round it to $1,900 we’ll dedicate to hitting. That leaves $1,220 to spend on pitching. I’ll only show you the hitting side, calculating pitcher values will be good practice for you.

As we mentioned before, we will be drafting 168 hitters. And we have $1,900 to distribute among those 168 hitters. You’ll see people do it differently but I always calculate mine out to the penny, even though you actually will be bidding whole dollars. I also exactly distribute the entire $1,900 over the 168 hitters I think should be drafted. Toward the end, of course, I see other teams choosing players I have negative values assigned to. I say don’t worry about it, this is your draft sheet. not theirs.

As you might have guessed, we will be using that total Z-score column to determine how much of our $1,900 each hitters should be allocated. But if you look at it closely(and if I had numbered the lines), you might notice that these values drop to zero at hitter No. 157. We didn’t worry about this we looking at rankings, all we cared about was comparative value. But now, we can’t have players we know will be drafted valued at a negative dollar figure. So easiest thing to do is re-zero our scale. Kind of like re-zeroing an actual scale say if you had a box on it but wanted to weigh only what was in the box. In our case, player No. 168 needs to have a positive value, and No. 169 needs to have a zero or negative value. Player No. 169 for us is Todd Helton, with total Z-score of -.462. So if we add .462 to every player, this should reset our scale.

Now that we have exactly 168 hitters with a positive Z-score sum, we add up the entire sum of these positive Z-scores. I get a total value for all hitters of 532.173. This is the realm over which our dollars need to be evenly distributed, so we’re dividing our $1,900 over these 532 values. So each unit of z-score is worth $3.57. We would then multiply our adjusted z-score by this amount to determine the dollar value. This should produce something like this:

I ran a quick sum and indeed the total values of hitters 1 through 168 is $1899.85. And that’s close enough. Again, I didn’t inflate hitter values versus pitcher values at all, if you think these look a little lower than you expected. Adjusting the ratio is very easy.

I hope this has been helpful. Many of the members here at the Cafe run their own projections and values so if you have questions, it’s very easy to start up a conversation about it. Best of luck in your leagues this year.

Ed. Note: Several duplicate entries were removed from tables that may slightly affect the math of the output listed. However, the article is focused on the process, which is still sound, and not the results.

 
Jason posts regularly here at the cafe under the user name TheRock.
 

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